Impossibility of What? Formal and Substantive Equality in Algorithmic Fairness

In the face of compounding crises of social and economic inequality, many have turned to algorithmic decision-making to achieve greater fairness in society. As these efforts intensify, reasoning within the burgeoning field of "algorithmic fairness" increasingly shapes how fairness manifests in practice. This paper interrogates whether algorithmic fairness provides the appropriate conceptual and practical tools for enhancing social equality. I argue that the dominant, "formal" approach to algorithmic fairness is ill-equipped as a framework for pursuing equality, as its narrow frame of analysis generates restrictive approaches to reform. In light of these shortcomings, I propose an alternative: a "substantive" approach to algorithmic fairness that centers opposition to social hierarchies and provides a more expansive analysis of how to address inequality. This substantive approach enables more fruitful theorizing about the role of algorithms in combatting oppression. The distinction between formal and substantive algorithmic fairness is exemplified by each approach's responses to the "impossibility of fairness" (an incompatibility between mathematical definitions of algorithmic fairness). While the formal approach requires us to accept the "impossibility of fairness" as a harsh limit on efforts to enhance equality, the substantive approach allows us to escape the "impossibility of fairness" by suggesting reforms that are not subject to this false dilemma and that are better equipped to ameliorate conditions of social oppression.